Why does the Torah switch from "Aharon" to 'ha'Kohen asher Yimshach oso ... "?
Rashi and Rashbam: Since throughout the Parshah, the Torah referred exclusively to Aharon, the Torah found it necessary to explain that the same applies to the Kohanim Gedolim who serve after him. 1
Because the Avodah on Yom Kipur is incumbent exclusively upon the Kohen Gadol (Rashi).
And why does the Torah add "va'asher Yemalei es Yado ... "?
Rashi and Seforno: To teach us that a Kohen Gadol who is initiated by wearing the eight Begadim 1 has the same Din as one who is anointed with the Shemen ha'Mishchah.
During the era of the second Beis-ha'Mikdash, when the Shemen ha'Mishchah was not available.
And what are the implications of "Lechahein Tachas Aviv"?
Rashi: This teaches us that if the Kohen Gadol's son is worthy to succeed his father, he has priority over all other contenders.
What is the Pasuk referring to when it writes that Aharon did everything that Hashem commanded Moshe?
Rashi #1, Ramban #1 and Rashbam: The Pasuk is teaching us that Aharon did everything mentioned above when Yom Kipur arrived.
Rashi #2: It means that Aharon wore the Bigdei Kehunah, not because of the Kavod that they afforded him, but in order to carry out the command of Hashem.
Ramban #2: It also teaches us that Aharon was careful never to enter the Kodesh Kodashim except on Yom Kipur with the prescribed Korbanos.